Abstract

A damage-dependent constitutive model for laminated composites has been developed for the combined damage modes of matrix cracks and delaminations. The model is based on the concept of continuum damage mechanics and uses second-order tensor valued internal state variables to represent each mode of damage. The internal state variables are defined as the local volume average of the relative crack face displacements. Since the local volume for delaminations is specified at the laminate level, the constitutive model takes the form of laminate analysis equations modified by the internal state variables. Model implementation is demonstrated for Ex and vxy of quasi-isotropic and cross-ply laminates. The model predictions are in close agreement to experimental results obtained for graphite/epoxy laminates.

References

1.
Kachanov
,
L. M.
, “
On the Creep Fracture Time
,”
Izvestia AN SSR, Otd. Tekhn. Nauk
; No.
8
,
1958
, pp.
26
-
31
, (in Russian).
2.
Onsager
,
L.
, “
Reciprocal Relations in Irreversible Process I.
,”
Physics Review
 0031-899X https://doi.org/10.1103/PhysRev.37.405, Vol.
37
,
1931
, pp.
405
-
426
.
3.
Rabotnov
,
Y. N.
,
Creep Problems in Structural Members
,
North-Holland
,
Amsterdam, The Netherlands
,
1969
.
4.
Bazant
,
Z. P.
, “
Mechanics of Distributed Cracking
,”
Applied Mechanics Reviews
 0003-6900, Vol.
39
,
1986
, pp.
675
-
705
.
5.
Krajcinovic
,
D.
, “
Continuum Damage Mechanics
,”
Applied Mechanics Reviews
 0003-6900, Vol.
37
,
1984
, pp.
1
-
6
.
6.
Krajcinovic
,
D.
, “
Update to Continuum Damage Mechanics
,”
Applied Mechanics Update 1986
,
Steele
,
C. R.
, and
Springer
,
G. S.
, Eds.,
The American Society of Mechanical Engineers
,
1986
, pp.
403
-
406
.
7.
Kachanov
,
L. M.
,
Introduction to Continuum Damage Mechanics
,
Martinus Nijhoff
,
Dordrecht
,
1986
.
8.
Talreja
,
R.
, “
A Continuum Mechanics Characterization of Damage in Composite Materials
,”
Proceedings of the Royal Society of London
, Vol.
399A
,
1985
, pp.
195
-
216
.
9.
Talreja
,
R.
, “
Residual Stiffness Properties of Cracked Composite Laminates
,”
Advances in Fracture Research, Proceedings of the Sixth International Conference de Fracture
, Vol.
4
,
New Delhi, India
,
1985
, pp.
3013
-
3019
.
10.
Talreja
,
R.
, “
Transverse Cracking and Stiffness Reduction in Composite Laminates
,”
Journal of Composite Materials
 0021-9983, Vol.
21
,
1985
, pp.
355
-
375
.
11.
Talreja
,
R.
,
Fatigue of Composite Materials
,
Technical University of Denmark
,
Lyngby, Denmark
,
1985
.
12.
Talreja
,
R.
, “
Stiffness Properties of Composite Laminates with Matrix Cracking and Interior Delamination
,”
Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark
, No.
321
,
03
1986
.
13.
Allen
,
D. H.
,
Harris
,
C. E.
, and
Groves
,
S. E.
, “
A Thermomechanical Constitutive Theory for Elastic Composites with Distributed Damage—Part I: Theoretical Development
,”
International Journal of Solids and Structures
 0020-7683 https://doi.org/10.1016/0020-7683(87)90107-7, Vol.
23
, No.
9
,
1987
, pp.
1301
-
1318
.
14.
Allen
,
D. H.
,
Harris
,
C. E.
, and
Groves
,
S. E.
, “
A Thermomechanical Constitutive Theory for Elastic Composites with Distributed Damage—Part II: Application to Matrix Cracking in Laminated Composites
,”
International Journal of Solids and Structures
 0020-7683 https://doi.org/10.1016/0020-7683(87)90108-9, Vol.
23
, No.
9
,
1987
, pp.
1319
-
1338
.
15.
Allen
,
D. H.
,
Groves
,
S. E.
, and
Harris
,
C. E.
, “
A Cumulative Damage Model for Continuous Fiber Composite Laminates with Matrix Cracking and Interply Delaminations
,”
Composite Materials Testing and Design: 8th Conference
, STP 972,
American Society for Testing and Materials
,
Philadelphia
,
1987
, pp.
57
-
80
.
16.
Allen
,
D. H.
,
Grove
,
S. E.
,
Harris
,
C. E.
, and
Norvell
,
R. G.
, “
Characteristics of Stiffness Loss in Crossply Laminates with Curved Matrix Cracks
,”
Journal of Composite Materials
 0021-9983, Vol.
22
,
1988
, pp.
71
-
80
.
17.
Weitsman
,
Y.
, “
Environmentally Induced Damage in Composites
,”
Proceedings of the 5th Symposium on Continuum Modeling in Discrete Structures
,
A. J. M.
Spencer
, Ed.,
Nottingham, United Kingdom
,
1985
.
18.
Groves
,
S. E.
, “
A Study of Damage Mechanics in Continuous Fiber Composite Laminates with Matrix Cracking and Internal Delaminations
,” Ph.D. thesis,
Texas A&M University
, College Station, TX,
12
1986
.
19.
Harris
,
C. E.
,
Allen
,
D. H.
, and
Nottorf
,
E. W.
, “
Modelling Stiffness Loss in Quasi-Isotropic Laminates Due to Microstructural Damage
,”
Journal of Engineering Materials and Technology
 0094-4289, American Society of Mechanical Engineers, Vol.
110
,
04
1988
, pp.
128
-
133
.
20.
O'Brien
,
T. K.
, “
Characterization of Delamination Onset and Growth in a Composite Laminate
,”
Damage in Composite Materials
, STP 775,
K. L.
Reifsnider
, Ed.,
American Society for Testing and Materials
,
Philadelphia
,
1982
, pp.
141
-
167
.
This content is only available via PDF.
You do not currently have access to this content.